Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions

Valerio Lucarini

doi:10.5194/egusphere-egu2020-9491

Abstract

&lt;p&gt;For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one; the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such instability is the ice-albedo feedback. Following an idea developed by Eckhardt and co. for the investigation of multistable turbulent flows, we study the global instability giving rise to the snowball/warm multistability in the climate system by identifying the climatic Melancholia state, a saddle embedded in the boundary between the two basins of attraction of the stable climates. We then introduce random perturbations as modulations to the intensity of the incoming solar radiation. We observe noise-induced transitions between the competing basins of attractions. In the weak noise limit, large deviation laws define the invariant measure and the statistics of escape times. By empirically constructing the instantons, we show that the Melancholia states are the gateways for the noise-induced transitions in the weak-noise limit. In the region of multistability, in the zero-noise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. Finally, we propose a new method for constructing Melancholia states from direct numerical simulations, thus bypassing the need to use the edge-tracking algorithm.&lt;/p&gt;&lt;p&gt;Refs.&lt;/p&gt;&lt;p&gt;V. Lucarini, T. Bodai, Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions, Nonlinearity 30, R32 (2017)&lt;/p&gt;&lt;p&gt;V. Lucarini, T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122,158701 (2019)&lt;/p&gt;

Highlights

In the late 1960’s and in the 1970’s, Budyko, Sellers, and Ghil [1–3] proposed the idea that the Earth, in the current astrophysical and astronomical con guration, supports two co-existing attractors, the warm (W) state, which is analogous to the one we live in, and the so-called snowball (SB) state, which is characterised by global glaciation and a globally averaged surface temperature of about 200–220 K
The results on the expectation value of the transition times are presented in gure 2, where we show that, τ σ agrees with the prediction of equation (8)
In order to show that this approach does work, we investigate the properties of K = 3 variants of the Ghil–Sellers diffusive model we studied in [45], differing with respect to the law of the stochastic perturbation impacting the energy balance of the climate system

Summary

Introduction

In the late 1960’s and in the 1970’s, Budyko, Sellers, and Ghil [1–3] proposed the idea that the Earth, in the current astrophysical and astronomical con guration, supports two co-existing attractors, the warm (W) state, which is analogous to the one we live in, and the so-called snowball (SB) state, which is characterised by global glaciation and a globally averaged surface temperature of about 200–220 K. Models of different levels of complexity ranging up to the state-of-the-art Earth system models currently used for climate projections agree on predicting the existence of multistability in the climate system and point to the fundamental mechanisms described above as responsible for it, as well as providing values for SW∗ →SB that are in broad agreement with those obtained using simple models [7–9]. We remark that both the concentration of greenhouse gases and the position of the continents have an impact on the values of SW∗ →SB and SS∗B→W and on the properties of the W and SB states [10]. High values of the concentration of CO2 seem to be needed to deglaciate from an SB state [11]

Objectives

Results

Conclusion